Okay, let's tackle this math problem. We're starting with 362381 and subtracting 67678.

Step 1: We'll start by subtracting the digit 8 and the borrow 0 from 1 in column 1 and get -7.
We add -7 to 10 and get 3 as the first digit of the result.

Step 2: We'll start by subtracting the digit 7 and the borrow 1 from 8 in column 2 and get 0.
0 is the next digit of our result.

Step 3: We'll start by subtracting the digit 6 and the borrow 0 from 3 in column 3 and get -3.
We add -3 to 10 and get 7 as the next digit of the result.

Step 4: We'll start by subtracting the digit 7 and the borrow 1 from 2 in column 4 and get -6.
We add -6 to 10 and get 4 as the next digit of the result.

Step 5: We'll start by subtracting the digit 6 and the borrow 1 from 6 in column 5 and get -1.
We add -1 to 10 and get 9 as the next digit of the result.

Step 6: We'll start by subtracting the digit 0 and the borrow 1 from 3 in column 6 and get 2.
2 is the next digit of our result.

So, 362381 - 67678 = 294703.